2 d 3)[(3x2 – 4x +7)(5x³ – 9x)®] dx - -

Q: 14. 3(x³+ 4x²) + 2x(x – 7) 15. 4(3d?+5d) - d(d² – 7d + 12) 16. 3(2t2- 4t- 15)+ 6t(5t +2)

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Q: 3 fx²³√₁² + x² dx X 2 a

A: Sol

Q: dx 4. 3 3 х3Vx2—9

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Q: (a) / (2.x4 + Vx3 + 4e* + + 8) dx - (b) / = x3 + 3x – 4 dx - x2 (c) (x + 4)(x³ – 9) dx .3 -

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Q: d³y --13 + 6y = 0 4 dx3 dx

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Q: evE -dr 3) Evaluate (6x² + 2æ – 3 4) Evaluate -dx p2(r + 3)

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Q: 3y = -x+6 %3D 2x + 4y = 12

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Q: d(-2x-1+ 6x7) -2 4x dx (3x5 + 4x) d dx 15x* + 4 3 d 16x dx 1 2 2

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Q: 8 (3x3 – 2a2 + 1) dx -3

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Q: Cos2 10x d 8.

A: The integral is given by,

Q: x- 3 +C 4 dx3D - 17+6x – x² +3arcsin = - V7+6x – x²

A: Show that ∫x7+6x-x2dx=-7+6x-x2+3arcsinx-34+C

Q: V72+5/7³+3x -dx

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Q: S(x*-3x3 +- -2)dx = x(8x*-30x3+5x-80) + C 1 %3D 40

A: Consider the right hand side of the given equation. The integration formula is  ∫xn=xn+1n+1+c

Q: (2) S dx x²√9-x²

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Зx3 +6x2+17х-5 dx х2+2х+5

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Q: 4. (D2 + 2D + 1Jy = 6

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Q: (D³ – D)y = –2(1+x) + 4e* – 6e¬* + 96e3x -

A: Given- D3-Dy=-21+x+4ex-6e-x+96e3x To Solve- The above differential equation.

Q: Pregunta 20 d x3 2x2 1 7x 3 - 8x3 - dx 3 O True

A: We have to show the given condition

Q: d. [(2x +1) (5a - 4)) dx 10x - 3 O 20x - 4 O 10x - 4 20x-3-

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Q: . 2 28x -15x dx 4x + 7. +C %3D

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Q: (c) / (3ré 3xe3x2+4x + 2e3a2. +4x dx 2 dx (d) 2х - 9

A: We solve this problem by using basic integration.  C part solve by substation method  And D is…

Q: (b) Evaluate 8x' +13x dx. (x² +2)²

A: Given integral is, ∫8x3+13xx2+22dx.   It is integrated as follows:   Apply the sum formula:…

Q: 3. (D² — 2D + 1) у %3 е* In a

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Q: cIn5 cln3 o 3x-y-3z dzdy dx = (b – 1) 3s 131:JNI Jigull %3D التكامل قيمة الثوابت الحقيقية a,b

A: We need to solve the given integral: ∫01∫0ln 5∫0ln 3e3x-y-3zdzddy dx This can be evaluated as…

Q: (z – 4ŋ³ at = 3 + 4i

A: Answer

Q: e* a) 16 +e2x dx xp b) | V3-2x2 dx c) x9x2-16 dx d) | x3x-2 dx e) - 8x + 20 dx x +9

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Q: xii. dx -x4 V3-2x-

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Q: - 4 + e-6x - dx e4x 23)

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Q: x* dx (9x² + 49) - (92 - - (9x* + 49) +c V9x² + 49 18.

A: This is a problem of integration. Based on the general formula we will solve the integral problem.

Q: x = u3 + 7 ; y= 6u? – 1 d²y ---> dx2

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Q: Question d²y Find if -9x – 3y = 8. %3D dx2

A: Detail solution is given below

Q: . АС%3Dх+5 BD=2x – 2 A

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Q: [D³ – D)y = -2(1+x) + 4e* - 6e¬* + 96e3× %3D

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Q: -10x4-9x3-48x2- 13x-48 dx - (x³ + 2x)(2x² + 3)

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Q: 8x dz +C %3D

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Q: 6. y = ekx 7. f(x) = (6x2 + 7x)4 8. g(t) = (4t² - 3t + 2)-2 %3D %3D

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Q: x2 dx is (ax2+4)(x2+9)

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Q: Find the derivative of function.

A: Differentiation of the function with respect to x helps to find the derivative of the function.…

Q: C. d. (3x + 2)(3x² + 4x)4 dx,u = 3x² + 4x [TV 7√7x − 1 dx,u = 7x − 1 -

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Q: - 48x3 – 80x2 – 70x – 126 dx Integrate: 16x2 + 25 + C

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Q: 4 5x2 Evaluate dx. TV3x2-1

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Q: (24+2x-x2)1/2dx

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Q: 2(5x-3)+2x=D2 (x+4)

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Q: 8x – 16 dx=2 x-2dx г- 2 (А) True в) False

A: The answer is True.

Q: d^x 2: +3. db4 3d ³ x db³ d²x -62 dx - 24x=0 db 27. db²

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Q: (ax-2) dx x2+ 2X + 15

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Q: (5x-5)dx 3x² - 8x - 3

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Q: 4 3/7) dx Find 4x* + - x6 + C

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Q: Sa4-2x3)5(4x3- 6x²) dx

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Q: 2) J (2x2 - 6x) dx B) - x3 - 3x2 +C + C D)를3-3x2+C + 3x + C

A: Here is the problem of integration  ∫( 2x² - 6x)dx  2x³/3 - 6x²/2 + C  2x³/3 - 3x² + C  So D is…